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Q.

A sphere of solid material of relative density 9 has a concentric spherical cavity and Just sinks in water. If the radius of the sphere be R, then the radius of the cavity (r) will be related to R as

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a

r3=89R3

b

r3=23R3

c

r3=83R3

d

r3=23R3

answer is A.

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Detailed Solution

Weight of the sphere = weight of water displaced43πR3−43πr39×g=43πR3×1×g 9R3−R3=9r3  or  9r3=8R3 ∴ r3=(8/9)R3
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